KASNEB Quantitative Analysis - Question 1c

The quarterly sales of Meshek Traders during the years 2022, 2023 and 2024 were as tabulated below: YearQuarterly Sales in Sh.“million” Q1Q2Q3Q42022457... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 2a

Outline FOUR applications of set-theory in business. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 2b

Find the area enclosed by the curve Y = 8X3 + 3X2 – 2X, the X axis and within the interval 2 ≤ X ≤ 4. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 2d

The amount of sales in millions of shillings for 92 companies in the construction industry was recorded as shown below: Sales (Sh.“million”)Number of... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 3a

Highlight FOUR characteristics of arithmetic mean. ... [Click to view full question and step-by-step solution]

KASNEB Quantitative Analysis - Question 6a

Explain THREE uses of time series analysis in business decision making. ... [Click to view full question and step-by-step solution]

August 2025

1a

Mathematical Techniques - Descriptive Statistics

Using appropriate formular, differentiate between “variance” and “standard deviation” as used in statistics.

1b

Probability

Customers arrive at a particular supermarket exit at the rate of 4 customers per minute. The distribution of arrivals approximate a Poisson distribution.

Required:

Determine the probability that:

(i) No customer arrives in a particular minute.

(ii) At least one customer arrives during a particular minute.

(iii) At most one customer arrives during a particular minute.

1c

Time series

The quarterly sales of Meshek Traders during the years 2022, 2023 and 2024 were as tabulated below:

Year	Quarterly Sales in Sh.“million”
	Q1	Q2	Q3	Q4
2022	45	78	56	80
2023	44	67	43	86
2024	53	89	81	102

Required:

(i) The three-quarter moving average.

(ii) The seasonal index for each quarter assuming the multiplicative model.

(iii) Derive the deseasonalised sales using the multiplicative model.

2a

Decision Theory

Outline FOUR applications of set-theory in business.

2b

Mathematical Techniques

Find the area enclosed by the curve Y = 8X3 + 3X2 – 2X, the X axis and within the interval 2 ≤ X ≤ 4.

2c

Probability

In a certain college, 30% of the students failed in statistics and 15% failed in mathematics while 10% failed in both statistics and mathematics in a given semester.

Required:

If a student is selected randomly, determine the probability that:

(i) The student failed in statistics given that he failed in mathematics.

(ii) The student failed in statistics or mathematics.

(iii) The student failed in neither statistics nor mathematics.

2d

Mathematical Techniques - Descriptive Statistics

The amount of sales in millions of shillings for 92 companies in the construction industry was recorded as shown below:

Sales (Sh.“million”)	Number of companies
10 – 20	3
20 – 30	7
30 – 40	13
40 – 50	X
50 – 60	27
60 – 70	Y
70 – 80	8

Required:

(i) Determine the value of X given that the median sales for the companies is Sh.51.4815 million.

(ii) Determine the value of Y given that the modal sales for the companies is Sh.54 million.

3a

Mathematical Techniques - Descriptive Statistics

Highlight FOUR characteristics of arithmetic mean.

3b

Probability

The probability of making a type I error on a certain washing machine is 0.10. The probability that the machine will remove all stains on a garment when there is a type I error is 0.30 and the probability that the machine will remove all stains on the garment when there is no type I error is 0.80.

Required:

Find the probability of type I error assuming that the machine fails to remove the stains.

3c

Correlation and Regression Analysis

A national healthcare agency conducted a study to investigate the relationship between the number of patients at the Nairobi region hospital compared to the total cost of healthcare during a period of 10 months. In the year 2024, the following data were obtained:

Month	Number of patients	Total cost (Sh.“000”)
January	170	150
February	150	165
March	220	225
April	265	220
May	160	150
June	120	115
July	100	95
August	165	160
September	150	90
October	110	105

Required:

(i) The Pearson’s coefficient of correlation between the number of patients attended and the total cost of healthcare. Interpret the results.

(ii) The coefficient of determination. Interpret the result.

4a

Probability

The use of internet has become a major component of a student’s day. A research study classified use of internet into 3 categories for students: No use, light use and heavy use. The study observed 1,000 students over a period of one month and developed the following transition matrix of probabilities from day to day:

		No use	Light use	Heavy use
	No use	0.35	0.15	0.50
Previous day	Light use	0.30	0.35	0.35
	Heavy use	0.15	0.30	0.55

Required:

Suppose that the initial distribution for the three categories is (0.20, 0.40, 0.40), find the distribution after:

(i) 1 day.

(ii) 2 days.

(iii) At steady state.

4b

Hypothesis Testing and Estimation

The data below shows the number of students enrolled in six universities for a business course before and after the course was advertised in a local newspaper:

University	Number of students before advertisement	Number of students after advertisement
A	170	180
B	145	151
C	150	143
D	170	177
E	172	178
F	164	167

Required:

Using the paired t-test, determine whether the advertisement was a success at a 1% level of significance.

5a

Mathematical Techniques - Matrix Algebra

Explain the following terms as used in the input-output analysis:

(i) Primary inputs.

(ii) Technical coefficients.

(iii) Final demand.

5b

Mathematical Techniques - Calculus

A milk production farm intends to undertake a research on a new type of feed which would increase the cow’s productivity. The monthly revenue in thousand shillings would be represented by R=−5X2+9X where X is the monthly milk produced and sold in thousand units.

Past records of cow’s production in the farm estimates its marginal costs in thousand shillings could be represented by the function MC=2X−2.

The fixed costs will be Sh.2,000 per month.

Required:

(i) The total cost function of the farm.

(ii) The profit function of the farm.

(iii) The break-even output of the farm.

(iv) The profit maximising output of the farm.

(v) The price that should be charged in order to maximise profit.

6a

Time series

Explain THREE uses of time series analysis in business decision making.

6b

Decision Theory

Jumbo Ltd. has to make a decision on whether to invest in project A, B or C. The economic conditions could be favourable, moderate or unfavourable.

The table below shows the potential payoffs in thousands of shillings (Sh.“000”) depending on the market conditions and their associated probabilities:

	Economic conditions
Project	Favourable	Moderate	Unfavourable
A	7,300	5,600	4,100
B	15,100	6,700	0
C	9,500	6,000	2,500
Probability	0.20	0.30	0.50

Required:

Advise the management of Jumbo Ltd. of the most optimal decision using:

(i) Maximax criterion.

(ii) Maximin criterion.

(iii) Laplace criterion.

(iv) Expected monetary value (EMV) criterion.

7a

Linear programming

Jojox Steel Limited manufactures black and white sheets of steel. A black sheet requires 12 minutes for moulding, 24 minutes for galvanizing, 18 minutes for rolling and 27 minutes for packaging. A white sheet requires 8 minutes for moulding, 6 minutes for galvanizing, 12 minutes for rolling and 60 minutes for packaging. The firm’s management monitors the production process times as it has a maximum of 126 hours for moulding, 120 hours for galvanizing, 142 hours for rolling and 540 hours for packaging. The selling price per sheet is Sh.4,000 for the black sheet and Sh.3,300 for the white sheet.

Required:

(i) Formulate the linear programming model to represent the above information.

(ii) Using the graphical method, solve the linear programming model formulated in (a) (i) above.

7b

Probability

The wages paid to workers of Baraka Ltd. are assumed to be normally distributed with a mean of Sh.37,000 and a standard deviation of 1,400.

Required:

Calculate the probability that an employee chosen at random earns salary of:

(i) More than Sh.39,000.

(ii) Less than Sh.33,500.

(iii) Between Sh.34,000 and Sh.40,000.

August 2025

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